Combine water and sugar in a saucepan.

Stir over low heat for 5 minutes until sugar dissolves.

Increase heat to high and boil for 5 minutes.

Cool for 30 minutes.

Puree watermelon in a blender.

Strain puree through a fine sieve to extract juice.

Add sugar syrup to watermelon juice and combine.

Pour into an airtight container, cover, and freeze for 5 hours until almost set.

Break up the sorbet with a fork and transfer to a food processor.

Process until smooth and icy.

Return sorbet to the container and freeze for 5 hours until firm.

Remove from the freezer and repeat the processing step.

Repeat the processing step, adding egg whites.

Process until smooth and paler in color.

Return the sorbet to the container and freeze until firm.

Scoop into serving bowls or waffle cones and serve immediately.